<p>This study introduces a geometrically nonlinear electromagnetic energy harvester employing symmetrical inclined springs. Precise adjustment of vertical spring spacing enables controlled configuration of either bistable or tristable potential wells and their depths. Global dynamic analysis of this energy harvesting system (combining extended averaging, Runge–Kutta, and cell-mapping methods) reveals resonant characteristics, potential-well transitions, and the evolution of basins of attraction (BAs) under harmonic base vibration. It is found that the tristable system enables voltage generation under ultra-weak vibrations near trivial equilibrium. By comparison, the bistable system achieves high-energy orbits with lower activation thresholds for high-energy intra-/inter-well states and sustains high-voltage output across a wider effective bandwidth. High-energy attractors demonstrate extreme sensitivity to initial states due to fractal basin boundaries, leading to unpredictable collapses to low-energy states that critically compromise reliability. The bistable configuration exhibits superior robustness across medium-to-high vibration amplitudes, attributed to its larger and contiguous BAs supporting high-output responses, which counters claims of tristable peak-voltage superiority under extreme base vibrations. These results provide theoretical support for guiding reliable optimization of geometrically nonlinear energy harvesters in low-frequency vibration environments.</p>

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Dynamics comparison of bistable and tristable configurations in a geometrically nonlinear electromagnetic energy harvesting system

  • Huilin Shang,
  • Qi Ding

摘要

This study introduces a geometrically nonlinear electromagnetic energy harvester employing symmetrical inclined springs. Precise adjustment of vertical spring spacing enables controlled configuration of either bistable or tristable potential wells and their depths. Global dynamic analysis of this energy harvesting system (combining extended averaging, Runge–Kutta, and cell-mapping methods) reveals resonant characteristics, potential-well transitions, and the evolution of basins of attraction (BAs) under harmonic base vibration. It is found that the tristable system enables voltage generation under ultra-weak vibrations near trivial equilibrium. By comparison, the bistable system achieves high-energy orbits with lower activation thresholds for high-energy intra-/inter-well states and sustains high-voltage output across a wider effective bandwidth. High-energy attractors demonstrate extreme sensitivity to initial states due to fractal basin boundaries, leading to unpredictable collapses to low-energy states that critically compromise reliability. The bistable configuration exhibits superior robustness across medium-to-high vibration amplitudes, attributed to its larger and contiguous BAs supporting high-output responses, which counters claims of tristable peak-voltage superiority under extreme base vibrations. These results provide theoretical support for guiding reliable optimization of geometrically nonlinear energy harvesters in low-frequency vibration environments.